We specialize in mathematical modeling, numerical analysis, numerical methods, computer simulations, and the development of open-source software libraries. We also focus on optimization, inverse analysis, stochastic methods, machine learning, parallel programming, and supercomputer calculations.
Research in the above areas is motivated by solving geoscientific problems of high societal importance. In particular, nonlinear multiphysics processes related to deep geological repositories of nuclear waste, geotechnical stability analysis, and compressed air energy storage are investigated. Our work is based on continuum mechanics, thermodynamic laws, and the finite element method. Other applications include seismic event classification and wildfire detection, where machine learning methods are used.
We strive for multidisciplinary research in collaboration with software library developers and experts in civil engineering, geotechnics, seismicity, and environmental sciences.
Research directions
Analysis and application of Biot and Biot-Barenblatt models
Development of mathematical models for hydro-mechanical processes in fractured rock masses
Applications of the finite element method and its variants for multiphysics problems
Iterative methods and preconditioning for saddle-point systems of equations
Uncertainty analysis using stochastic methods
Development of open-source finite element codes
Estimation of damage zones caused by deep mining and their influence on multiphysics processes
Development of thermodynamically consistent poro-elastoplastic models for bentonite and other swelling clays
Application of thermo-hydro-mechanical models for simulation of saturation processes in sealing barriers of deep geological repositories for spent nuclear fuel
Development of experimental codes in COMSOL Multiphysics and other software libraries
Variational formulations and solvability analysis of elastoplastic problems
Development of mathematical theory for limit analysis and strength parameter reduction methods
The finite element method and related convergence analysis and a posteriori error estimates
Development of innovative optimization methods, continuation techniques, and iterative solvers
Convergence analysis for Newton-type methods
Stability analysis of slopes, embankment dams, foundations, and tunnels
Influence of the seepage on geotechnical stability analysis
Development of experimental codes in MATLAB and Python for solving elastoplastic problems and geotechnical stability analysis
Collaboration with developers of commercial and non-commercial software for solving geotechnical problems
Development, implementation and optimization of efficient solvers for quadratic programming
Development and implementation of massively parallel solvers based on FETI and BETI domain decomposition methods
Development of solvers for machine learning of the support vector machines type
Use of supercomputers in demanding numerical simulations
Applications of the PERMON library, e.g. for solving problems of contact mechanics, machine learning and other problems leading to quadratic programming
Cooperation with developers of the sw platform PETSc
Development of Bayesian inversion techniques based on surrogate models and the delayed acceptance Metropolis-Hastings algorithm
Construction of surrogate models using neural networks
Development of the universal software library surrDAHM implementing the aforementioned methods
Application of the surrDAHM library to solve multiphysics problems
Simulation of processes described by partial differential equations with uncertain input data using the stochastic Galerkin method
Development of innovative numerical methods for efficient solution of problems arising from the use of the stochastic Galerkin method
Application of a certified methodology in the environment of the Bukov Underground Research Facility and its further development based on experimental observations
Development of numerical solvers for inverse analysis reducing the influence of noise in measured data
Development of a software library for solving 3D elastic problems with complex geometry
Development of measuring equipment based on LIDAR technology and its usage for convergence measurements of displacements on tunnel walls
Detection of wildfires using support vector machines and other machine learning techniques
Classification of seismic events using advanced neural networks
Automatic detection and localization of seismic events
Development of an application supporting seismic services using machine learning
Development of a mathematical model and its implementation in MATLAB
Development of a prototype of the proposed device in a smaller scale
Cooperation with industrial partners
Analysis of mechanical degradation of the disposal canister with respect to material weakening due to corrosion
Numerical simulations of long-term temperature fields around the deep repository
